This invention is related to the field of error-correction decoders, and more particularly to such decoders known as threshold decoders.
Coded data transmissions have conventionally been decoded by a number of techniques, most of which rely upon digital methods and algorithms for their implementation. One very practical type of decoding is known as threshold decoding, and threshold decoding techniques have been classified into Type I and Type II. In Type I, the parity sequences are recalculated from the received information bits and the recalculated parity bits are compared with the received parity bits with the results of the comparisons being stored in a syndrome register. Thus, the syndrome register will contain a plurality of indications representing agreement or disagreement between the received and recalculated parity bits. Appropriate stages in the syndrome register are polled and a decision is then made to either complement the received information bit or let it stand as is.
In the Type II decoder, the parity sequences are not recalculated, but the received information and parity bits are stored in a register. Appropriate combinations of the received information and parity bits are used to obtain a plurality of independent estimates of each received bit, and a decision as to the value of that bit is made based upon a polling of these plural estimates.
In most cases, threshold decoding techniques have been digitally implemented using hard detection. In hard detection, the received bit is assigned either a "0" or "1" binary value based upon whether it is above or below a predetermined threshold level. For example, in binary antipodal signalling employing voltage levels of +1 and -1 volts, a 0-volt threshold level would be used to determine the value of each received bit. A disadvantage of digital decoding techniques utilizing hard detection is that there is useful decoding information in the level of the received signal which is lost after the hard detection is performed. For example, a received voltage level of +1 volts would almost assuredly represent a transmitted +1 volt signal, but a received voltage level of 30 0.2 volts is much more questionable, but both would be decoded as the same value. In codes which are majority logic decodable, i.e. codes utilizing parity bits calculated from some combination of the information bits such that the received information bits can be decoded by polling either a plurality of independent estimates of the bit value itself or a plurality of independent estimates of the accuracy of the received bit value, significant coding gains could be achieved by weighting the various estimates in accordance with the reliabilities of the terms used to arrive at those estimates. In general, for example, a bit estimate obtained by a combination of various received bits each of which had a voltage level of approximately +1.0 volts would be much more reliable than an estimate obtained from a plurality of bits each having voltage levels of approximately +0.2 volts.
Some decoding techniques have been proposed in which soft detection is used to assign reliability weights to the various received bits. For example, approximate a posteriori probability (APP) decoding techniques employ 3-bit soft decisions. Conventional hard-decision threshold decoding is performed and the soft decision is utilized to weight either the conventional parity checks or the decoding threshold value. The use of soft decisions to reliability weight a digital decoding process, however, is somewhat difficult due to the necessity of maintaining a separate calculation loop solely for the reliability factors.
Recognizing the inherent reliability information in the analog values of the received bits, I previously devised an analog threshold decoding system which utilizes analog shift registers, analog multipliers and analog summation in generating the estimates of the received information bits. Such a system is disclosed in my U.S. Pat. No. 4,130,818, assigned to the same assignee as the present invention. The analog threshold decoding technique achieves improvements in coding gain since it utilizes the reliability information which is inherent in the analog received voltages. However, although the analog threshold decoding does make use of this inherent reliability information, it does not utilize this information in an optimal manner.